Using hcipy, the High Contrast Imaging package for Python[1]}, we simulated three test case atmospheres: two with single layer atmospheres with a wind speed of 7 m/s (split into \(v_x, v_y = 2.13, 6.67\) ) and 14 m/s (split into \(v_x, v_y = 2, 13.5\) ), and one that included 8 layers according to a C\(_N^2\)  and wind velocity study of Maunakea weather[2]}. The layers and heights from this profile are described in Table REF ; all layers in the multi-layer simulation had a random direction assigned. For the purposes of this simulation we used an 8 meter primary mirror diameter, an \(r_0=15\) cm at 500nm, simulated at a resolution of 48 by 48 pixels (which maps to an idealized wavefront sensor of 48 by 48 pixels), and evolved with a \(0.5\) ms time step. This simulates a Gemini Planet Imager-like system, which was the instrument for the original PFC simulations[3]}. We consider an idealized wavefront sensor whose output is exactly the simulated 48 by 48 pixel phase screen at a given time step. I.e., we use a perfect wavefront sensor (there is no difference between the phase screen and the phase screen we sense) and a perfect deformable mirror (there is no difference between the phase screen we predict and the correction we apply) and focus only on how faithfully we can predict the wavefront given a choice of time delay.
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